Periodic Forcing of a System near a Hopf Bifurcation Point

Periodic Forcing of a System near a Hopf Bifurcation Point

Bibliographic Details
Main Author: Zhang, Yanyan
Language:English
Published: The Ohio State University / OhioLINK 2010
Subjects:
Mathematics
Hopf bifurcation
Periodic forcing
S1 symmetry
Liapunov-Schmidt reduction
Normal Form
Universal unfolding
Singularity theory
Transition set
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-osu12911747952021-08-03T06:01:01Z Periodic Forcing of a System near a Hopf Bifurcation Point Zhang, Yanyan Mathematics Hopf bifurcation Periodic forcing S1 symmetry Liapunov-Schmidt reduction Normal Form Universal unfolding Singularity theory Transition set We study a periodically forced system of ODEs near a point of Hopf bifurcation, where the forcing is pure harmonic with small amplitude. We assume that the ratio of the Hopf frequency of the ODE system and the forcing frequency is close to k/l where k and l are coprime. We look for all small periodic solutions of the forced system as the forcing frequency varies. In other words, we examine the influence of the forcing frequency on the number of periodic solutions to the forced system. This problem is complicated because of the existence of three small parameters: the amplitude of the forcing, the deviation of the bifurcation parameter from the point of Hopf bifurcation, and the deviation of the ratio of the Hopf and forcing frequencies from a rational number. Our results are presented in terms of bifurcation diagrams of amplitude of periodic solutions versus the forcing parameter for fixed forcing amplitude and Hopf parameter. 2010-12-17 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795 http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Mathematics
Hopf bifurcation
Periodic forcing
S1 symmetry
Liapunov-Schmidt reduction
Normal Form
Universal unfolding
Singularity theory
Transition set
spellingShingle Mathematics
Hopf bifurcation
Periodic forcing
S1 symmetry
Liapunov-Schmidt reduction
Normal Form
Universal unfolding
Singularity theory
Transition set
Zhang, Yanyan
Periodic Forcing of a System near a Hopf Bifurcation Point
author Zhang, Yanyan
author_facet Zhang, Yanyan
author_sort Zhang, Yanyan
title Periodic Forcing of a System near a Hopf Bifurcation Point
title_short Periodic Forcing of a System near a Hopf Bifurcation Point
title_full Periodic Forcing of a System near a Hopf Bifurcation Point
title_fullStr Periodic Forcing of a System near a Hopf Bifurcation Point
title_full_unstemmed Periodic Forcing of a System near a Hopf Bifurcation Point
title_sort periodic forcing of a system near a hopf bifurcation point
publisher The Ohio State University / OhioLINK
publishDate 2010
url http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795
work_keys_str_mv AT zhangyanyan periodicforcingofasystemnearahopfbifurcationpoint
_version_ 1719429498221363200

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